Aging dynamics in globular proteins: summary and analysis of experimental results and simulation by a modified trap model.

Recent results of spectral diffusion experiments by spectral hole-burning techniques carried out at cryogenic temperatures on various monomeric heme proteins unequivocally show interesting new features of conformational dynamics of globular proteins that were not emphasized in the literature until now. These new aspects of the protein dynamics are anomalous diffusion and the aging effect. Here, using the similarities between proteins and glassy systems, we present a model which can interpret the line broadening and-through this effect-the aging phenomenon as well. Leaving untouched the widely accepted energy landscape (EL) concept for the general description of protein dynamics, we concentrate on the bottom of the funnel-like EL, because this part corresponds to the native state(s) at low temperature. We suggest that the overall shape of the EL at the lowest energy range is rather smooth, but on a finer scale it consists of traps. The dynamics is defined by sequential jumps among these traps and the process is described by a Master equation, where the hopping rate only depends on the parameters of the starting state. This model was adapted to interpret the common results of spectral diffusion experiments. We tested our model in the simplest case by computer simulation, and it shows excellent agreement with the experimental data. To our knowledge this is the first work where a theoretical interpretation of the aging dynamics of proteins is directly and quantitatively related to the experimental observations. We also show that the model, after the generalization that the traps are hierarchically organized, is in accordance with the concept of other well-known EL models.